Not sure I understand. You have BT on your HA. It works fine. You want an “old fashioned” landline that also works w. BT? I assume there is such an item. Do a search on Amazon. There seem to be landline phones that do BT - but didn’t look at details to see if they do what you want. I would think that altho landlines are becoming more extinct for home use - they will be around for a long time on the business front - so features will keep being developed.
Panasonic makes several landline phones that are Bluetooth capable and I’m sure other companies have them too.